An interval type-2 fuzzy technique for order preference by similarity to ideal solutions using a likelihood-based comparison approach for multiple criteria decision analysis

The technique for order preference by similarity to ideal solutions (TOPSIS) is a well-known compromising method for addressing decision-making problems. In general, incomplete preference information and vague subjective judgments are realistic in practice. Accordingly, the theory of interval type-2 fuzzy sets has received increasing attention in the decision-making field because of its great ability to handle imprecise and ambiguous information in a convenient manner. The purpose of this paper is to develop a novel interval type-2 fuzzy TOPSIS method for multiple criteria decision analysis that is based on interval type-2 trapezoidal fuzzy numbers. This paper introduces the concept of approximate positive-ideal and negative-ideal solutions and presents a simple way to approach the evaluative ratings of ideal solutions using interval type-2 trapezoidal fuzzy numbers. Based on the likelihoods of interval type-2 trapezoidal fuzzy binary relations, this paper proposes certain likelihood-based comparison indices to establish a likelihood-based closeness coefficient of each alternative relative to the approximate ideals. Applying a likelihood-based comparison approach with the approximate ideals, this paper develops the interval type-2 fuzzy TOPSIS procedure to determine the priority ranking orders of the alternatives under consideration of the multiple criteria evaluation/selection. Three practical applications involving landfill site selection, supplier selection, and car evaluation are examined to show the effectiveness and practicability of the proposed method. Furthermore, this paper makes a comparison of the solution results yielded by other interval type-2 fuzzy decision-making methods. The comparative analyses demonstrate that the proposed interval type-2 fuzzy TOPSIS method is easy to implement and produces effective and valid results for solving multiple criteria decision-making problems.